Global Gevrey solution of 3D anisotropic Navier-Stokes system in a strip domain

Abstract

We investigate the three-dimensional (3D) incompressible anisotropic Navier-Stokes system with dissipation only in the horizontal variables, posed in a strip domain. To overcome the difficulties arising from the boundary terms and the absence of vertical dissipation, we impose a Gevrey-class regularity condition in the vertical direction. For the remaining directions, we prove that the solution exhibits space-time analytic or Gevrey-class regularization. Furthermore, the solution is shown to possess an enhanced Gevrey regularity in the direction of strong diffusion, which is unconstrained by boundaries.